Determine the angular velocity of the Wheel

1. The problem statement, all variables and given/known data
The cart has a velocity vc = 3.4 ft/sec to the right. Determine the angular speed N (positive if counterclockwise, negative if clockwise) of the wheel so that point A on the top of the rim has a velocity (a) equal to 3.4 ft/sec to the left, (b) equal to zero, and (c) equal to 6.8 ft/sec to the right.

I have attached an image of the question

2. Relevant equations

3. The attempt at a solution

vA = vO + vA/O

vO = -3.4i

v = wXr

r = 11.6j

For part a)

-3.4i = 3.4i + wX<11.6j>

Solving for w gives me

w = 6.8/11.6 k rad/sec

Which is equivalent to

w = 5.597 rev/min

I don't think this is right and I can't see what's wrong with what I've done.